Minimum detectable effect size for main outcomes (accounting for sample
design and clustering)
Using the power calculation from Gerber and Green (2012), beta=normdist{effect size*sqrt(N)/(2*sigma) - normsinv(1-alpha/2)}, we want to achieve a power of 0.8, that is, beta=0.8, N=100, the level of significance alpha=0.05. From the literature, we find the standard deviation of the discount rate elicited is around 1.255. Using the above formula, we can calculate the effect size equals 0.703, which is 56% of the standard deviation.